Let, #f(t)=g(t)+h(t), g(t)=sin(t/16), h(t)=cos(t/18).#

We know that #2pi# is the **Principal Period** of both #sin, &, cos#

functions (funs.).

#:. sinx=sin(x+2pi), AA x in RR.#

Replacing #x# by #(1/16t),# we have,

# sin(1/16x)=sin(1/16x+2pi)=sin(1/16(t+32pi)).#

#:. p_1=32pi# is a period of the fun. #g#.

Similarly, #p_2=36pi# is a period of the fun. #h#.

Here, it would be very important to note that, #p_1+p_2# is **not**

the period of the fun. #f=g+h.#

In fact, if #p# will be the period of #f#, if and only if,

#EE l, m in NN," such that, "lp_1=mp_2=p.........(ast)#

So, we have to find

#l,m in NN," such that, "l(32pi)=m(36pi), i.e.,#

#8l=9m.#

Taking, #l=9, m=8,# we have, from #(ast),#

#9(32pi)=8(36pi)=288pi=p,# as the **period** of the fun. #f#.

**Enjoy Maths.!**